Abstract: In a few recent years there was growing interest in propagation of nonlinear waves in media with gain and losses. These are systems with the parity-time (PT) symmetry, with localized gain or dissipation, with imbalances gain and dissipation but still allowing for linear real spectra, etc. Physically the respective models are relevant to optics, plasmonics, Bose-Einstein condensates, atomic gasses, mechanical systems, electric circuits, etc. This Minisymposia aims to joint researches working in the related areas ranging from experimental and theoretical physics to mathematics.

MS-Tu-D-42-113:30--14:00Stationary states of unidirectional optical wave guidesCartarius, Holger (Univ. of Stuttgart)Abstract: Nonlinear PT-symmetric optical wave guides have shown to exhibit the effect of unidirectionality, which is usually studied in terms of propagating waves. We investigate this effect in the context of stationary states. In a mathematically equivalent system, viz. a Bose-Einstein condensate in a PT-symmetric double-well potential, it is well known that these stationary states possess complicated stability properties influenced by the nonlinearity. The relations of these two effects are analyzed.

MS-Tu-D-42-214:00--14:30PT symmetric nonlinear metamaterialsWunner, Guenter (Inst. of Theoretical Physics, Univ. of Stuttgart)Abstract: Although originally discussed in the context of non-Hermitian quantum mechanics, PT symmetry has been demonstrated experimentally in optics and other areas. Recently, PT symmetry has also entered the experimental f ield of metamaterials (see, e.g., Lawrence et al, Phys. Rev. Lett 113, 093901 (2014)). Investigations so far have been restricted to linear wave propagation in metasurfaces. In this paper we will study the effects of nonlinearity on PT symmetry in metamaterials.

MS-Tu-D-42-314:30--15:00PT-Symmetric Nonlinear Metamaterials with Nonlocal Interactions, N. Lazarides & G.P. TsironisLazarides, Nikos (Univ. of Crete)Abstract: PT-symmetric nonlinear metamaterials relying on gain and loss and comprising split-ring resonators (SRRs) have been recently introduced. In the presence of nonlinearity, they support gain-driven, breather-like excitations. In most SRR-based metamaterial models, the dipole-dipole interaction between SRRs is limited to nearest neighbors. However, the nonlocal interelement interaction affects significantly both the linear and nonlinear properties PT metamaterials. In the presence of nonlinearity, it may generate novel solutions not appearing in locally coupled metamaterials.

MS-Tu-D-42-415:00--15:30Integrable Nonlocal Nonlinear Schrödinger EquationMusslimani, Ziad (Florida State Univ.)Abstract: A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contrasted with the classical nonlinear Schrödinger equation.